Real Exchange Rates and the Balance of Trade: Does the J-curve Effect Really Hold?

Abstract

In this paper, we re-examine the relationship between trade flows, real effective exchange rates, and incomes by using the bilateral trade flows of 33 countries that form more than two-thirds of total world trade. For each country, we consider the bilateral trade flows of the country under consideration vis-à-vis all other countries. The analysis reveals the fact that for most of the countries, a real depreciation of the home currency has favorable effects on the home country’s trade balance in the long run. This long-run effect manifests itself in the short run for a small number of countries, indicating the fact that satisfying the Marshall-Lerner condition in the short run is more difficult. However, there is no evidence for the J-curve phenomenon, which suggests an initial deterioration in the trade balance in the short run following a depreciation.

1 Introduction

In this paper, we re-examine the relationship between aggregate trade flows, real effective exchange rates, and incomes by using a panel of 33 countries. A key issue in this literature is the extent to which trade flows are responsive to real price changes, more specifically, whether currency depreciation improves the trade balance, i.e., whether the well-known Marshall-Lerner (ML) condition, a condition that is typically considered to be a long-run phenomenon, holds. On the other hand, the J-curve hypothesis, introduced in the literature by Magee (1973), asserts that it is also possible for a depreciation to worsen the trade balance in the short run before contributing to its improvement in the long run (see Rose and Yellen 1989).¹

Several studies have attempted to distinguish the short-run effects of depreciations from their long-run counterparts to assess the validity of the J-curve hypothesis. A comprehensive review of the literature is provided by Bahmani-Oskooee and Ratha (2004) and Bahmani-Oskooee and Hegerty (2010). In this context, the short-run and the long-run effects of currency depreciation on the trade balance have largely been investigated by two lines of research. The first line employs trade balance data at the aggregate level between one country and the rest of the world.² The second and relatively more recent line of research uses trade data at the bilateral level between one country and its major trading partners (see, among others, Bahmani-Oskooee and Wang (2006) and Bahmani-Oskooee et al. (2005), and the references cited in Bahmani-Oskooee and Hegerty (2010)). Rose and Yellen (1989) were among the first to note the merits of using bilateral disaggregated versus aggregated data. They argued that since using aggregate trade data leads to the so-called “aggregation bias problem”, one would need to use trade data and the exchange rate at the bilateral level to test the J-curve hypothesis. Not only has this line of research not provided conclusive evidence for the J-Curve pattern, but it has also failed, in many cases, to support any long-run relation between the trade balance and the real exchange rate.³

In this paper, we reconsider this literature by using the bilateral trade flow data of 33 countries that form more than two-thirds of total world trade. We estimate the long- and short-run dynamics for each country separately by using a panel of its trading partners. Our estimations reveal the fact that the real depreciation of the home currency has favorable effects on the home country’s trade balance in the long run; hence, the ML condition holds. On the other hand, our analysis does not support the J-curve hypothesis.

The remainder of this paper is organized as follows. Section 2 outlines the model and the method used in its estimation. Section 3 describes the data and reports all of the results of our econometric analysis, as well as their interpretations. Section 4 concludes the paper.

2 The Model and Estimation Methods

We use a panel specification for the estimation of the trade balance model for each of the 33 countries. For each country, a panel trade balance model is estimated using the bilateral trade flows between the country and its trading partners. The classical workhorse trade balance model for country i, can be expressed as follows.⁴

$$\begin{array}{@{}rcl@{}} b^{i}_{jt}&=&{\rho^{i}_{j}} + {\mu^{i}_{j}} t + {\alpha^{i}_{j}} {y^{i}_{t}} +{\beta^{i}_{j}}e^{i}_{jt} +{\gamma^{i}_{j}}y_{jt} + u^{i}_{jt},\\ t&=&1,2,...,T; \quad i,j = 1,...,N; \quad i \neq j \end{array} $$

(1)

where N represents the number of countries and their trading partners included in our analysis, T is number of time periods, and t, as one of the regressors, is the common (cross-sectionally invariant) linear trend term. All variables are expressed in logarithms, and $b^{i}_{jt}$ represents (the logarithm of) the balance of trade of country i vis-à-vis country j, defined as the ratio of nominal exports and imports of country i to and from country j s at time t. Therefore, an improvement in the trade balance can be represented by an increase in $b^{i}_{jt}$, whereas a deterioration leads a decrease in its value. ${y^{i}_{t}}$ refers to country i’s income, whereas $y^{i}_{jt}$ represents the income levels of country i’s trade partners (country j s), and $e^{i}_{jt}$ denotes the real exchange rate of country i with respect to country j at time t. The real exchange rate is defined, in the usual manner, as the nominal exchange rate times the ratio of the foreign (j) and home (i) country price indices, where nominal exchange rates are expressed in units of domestic currency per unit US dollars. Hence, a decrease (increase) in the value of the real exchange rate indicates the appreciation (depreciation) of home country i’s currency with respect to country j’s currency. Therefore, the expected signs of the coefficient ${\gamma ^{i}_{j}}$ and ${\beta ^{i}_{j}}$ are positive, whereas a negative sign should be expected to be associated with αⁱ for all i s.

Equation (1) provides us a framework to estimate ${\gamma ^{i}_{j}}$ and ${\beta ^{i}_{j}}$ for each country i separately by using appropriate panel data estimators. The parameters are allowed to vary over j s, trading partners of country i to take into account cross-country (trade partner) heterogeneity. Allowing cross-country heterogeneity aims to capture the possible differences in the response of the trade balance of country i to the changes in the real exchange rates and incomes of its trading partners. Another important concern in our context is controlling for cross-sectional correlation, i.e., the interdependence across trading partners. It has been shown that this interdependence, i.e. the correlation across cross section units may have serious consequences if not accounted for.⁵

We account for these interdependence influences, or cross section correlation by using the common correlated effects (CCE) estimator of Pesaran (2006), which has become very popular in the empirical literature with a large number of applications. The approach has also been shown to work under very general conditions, including models with weak factors, dynamic models and even models with non-stationary data (see, for example, Chudik et al. 2011; Chudik and Pesaran 2013; Kapetanios et al. 2011; Persaran and Tosetti 2011; Pesaran et al. 2013).

To control for cross-sectional correlation, we incorporate the possible unobserved common effects into the model by using the error term, $u^{i}_{jt}$, for which the following multi-factor structure is assumed, for each i. Therefore, omitting the i subscripts for notational simplicity, we have the following:

$$ u_{jt}=\lambda_{j} \bold{f}_{t}+\varepsilon_{jt}, $$

(2)

where f_t is an m × 1 vector of the unobserved common factors common to all countries and ε_jt are the individual specific (idiosyncratic) errors.⁶

Given the parameter heterogeneity, to assess the overall effects of real exchange rates (of foreign incomes) on the trade balance of country i, we focus on the estimation of the average value of β_j (γ_j), namely, E(β_j) = β (E(γ_j) = γ), assuming a random coefficient model, $\beta _{j}=\beta +{\eta ^{1}_{j}}$ ($\gamma _{j}=\gamma +{\eta ^{2}_{j}}$), for all i’s, where $\eta ^{1,2}_{j}$s are assumed to follow an i.i.d. process.

The CCE estimation of Eq. (1) is based on OLS regressions in which the cross-sectional averages of all variables, including the regressand, are included as additional variables to approximate the unknown common factors. In CCE estimation, although the observed common factors, i.e., the intercept, time trend and y_t are included explicitly, the unobserved common factors, f_t are approximated by cross-sectional averages, $\overline {b}_{t}$, $\overline {e}_{t}$ and $\overline {y}_{t}$.

In this paper, the mean value of β_j and γ_j are estimated by the pooled (identical slopes) version of the CCE (CCEP) estimator of Pesaran (2006). CCEP, as a pooled estimator, is preferable when the individual slope coefficients are in fact the same so that the efficiency gains from pooling observations over the cross-section units can be achieved. Since we assumed, at least in the long run, a homogeneous response of the real exchange rate to the trade balance across countries, we simply adopt the CCEP estimator to achieve this efficiency. An alternative would be to adopt the mean group CCE estimator (CCEMG),⁷ which is a simple average of the β_j and γ_js, i.e., individual CCE estimators, over j s. Naturally, CCEMG should be used when the individual slope coefficients are thought to be different across cross-section units (hence, the overall effects can only be captured by averaging individual cases). We use CCEMG estimators when we estimate short-run effects, which are assumed to be different across trading partners.

As shown by Kapetanios et al. (2011), CCE estimators are consistent regardless of whether f_t is I(0) or I(1), given that u_jt is stationary⁸ and the number of unobserved factors is a fixed number. For each country i in our data set, we also test whether u_jt in (1) is stationary , which is accomplished by using cross-sectionally augmented panel unit root (CIPS) tests. The CIPS test, due to Pesaran (2007), is also valid when the series are cross-sectionally dependent, as with CCE estimators. The CIPS test follows the CCE approach and eliminates the cross-sectional dependence by augmenting the ADF (CADF) regressions with cross-sectional averages in an approach similar to CCE estimators.

The short-run dynamics is modeled by the following panel error correction model. For each country i, we have the following:

$$\begin{array}{@{}rcl@{}} {\Delta} b_{j,t} &=& \mu_{j}+\sum\limits_{l = 0}^{z}{\kappa^{l}_{j}}{\Delta} y_{t-l} +\sum\limits_{l = 1}^{s}\varphi^{b,l}_{j}{\Delta} b_{j,t-l}+ \sum\limits_{l = 0}^{q}\varphi^{e,l}_{j}{\Delta} e_{j,t-l}\\ &&+ \sum\limits_{l = 0}^{p}\varphi^{y,l}_{j}{\Delta} y_{j,t-l}+ \phi_{j} \hat{u}_{j,t-1}+ \xi_{j,t}, \end{array} $$

(3)

where $\hat {u}_{j,t-1}$ is the estimated residuals of (1). Δ, as usual, refers to the first-difference operator, and the coefficient ϕ_j provides a measure of the speed of adjustment of the trade balance to deviations from the long-run equilibrium described in (1).

3 Data

The data used in this paper are disaggregated (bilateral) trade data for a total of 33 countries. We use the bilateral trade flows of each of these 33 countries to obtain their bilateral trade statistics vis-à-vis their trading partners, which are accepted to consist of the remaining 32 countries in our data set. Table 1 illustrates the share of the bilateral trade flows of the 32 trading partners in the total trade of each country. As shown by the table, these shares vary between 64 to 94 and substantially cover the bulk of the bilateral trade flows for each of the countries in our data sets. On the other hand, the total bilateral trade flows among the 33 countries considered in this study form almost two-thirds of total world trade. The bilateral trade flows of each countries are taken from Direction of Trade Statistics published by the IMF. The sources of all of the countries included in the analysis for the output, prices and exchanges rates are International Financial Statistics and the data set supplied by the University of Cambridge, Centre for Financial Analysis & Policy, GVAR toolbox website (http://www.cfap.jbs.cam.ac.uk/research/gvartoolbox/), which is also used by Pesaran et al. (2009). We employ quarterly data covering the period of 1981q1-2010q2 for all countries.

Table 1 Countries and trading partners’ share in their total trade

4 Results of the Econometric Analysis

Following the estimation procedure in Holly et al. (2010), we first test the time series properties of the variables in the analysis by using CIPS unit root tests. Then, we estimate the parameters of the long-run relationship in (1) using CCE estimators and obtain the residuals. Finally, after checking the stationarity of these residual by using CIPS panel unit root tests, we estimate the parameters of the panel error correction Eq. (4) utilizing CCE estimators once again.

For each country i, the time series properties of b_jt, y_jt, e_jt are analyzed by using CIPS panel unit root tests, and in the case of y_t standard time series, ADF tests are used.⁹ Overall, the same conclusion emerges from the CIPS test results for all 33 countries in our analysis. They convincingly indicate that although the unit root hypothesis cannot be rejected for all of the real output (either in panel or time series unit root tests), the results for the trade balance and real effective exchange rates are not unambiguous and exhibit variations across countries, and the underlying lags used CADF regressions. This result is not surprising from an economic perspective, considering that the hypothesis of a unit root in both the trade balance and the real exchange rate is a matter of debate. On the other hand, as noted above, since CCE estimators are robust to the mixed time series properties of the underlying regressors, this result does not constitute a concern for the econometric procedure used in this study (see Kapetanios et al. 2011).¹⁰

4.1 Estimation of the Long-run Response of the Trade Balance

Table 2 displays the CCEP estimation results of the long-run trade balance Eq. (1) for the 33 countries; we report the coefficient estimates of the real exchange rate and income together with their t statistics.¹¹ As shown by the table, in 25 countries, with the exception of the Belgium, Norway, Switzerland, Canada, South Africa, Argentina, Saudi Arabia, and Philippines the real exchange rate appear to have significant long run effects on the trade balance. In 23 of them, with the exception of Mexico and Peru, the real depreciation of the domestic currency leads to an improvement in the trade balance in the long run, supporting the validity of Marshall-Lerner condition. For most of the countries, the results indicate an improvement in the trade balance of more than 1 percent as a result of 1 percent real depreciation. Only in the US, UK, France, Spain, and Singapore this impact on the trade balance appear to be less than 1 percent. Large improvements that are greater than 3 percent are observed in Chile, Indonesia, Thailand and Turkey.

Table 2 The long-run trade balance equation estimation results

To test the stationarity of the residuals of the long-run trade balance equation, for each country, we compute the CIPS panel unit root test statistics for the estimated residuals, computed as:

$$ \hat{u}_{j,t}=b_{j,t}-\hat{\rho}_{j} - \hat{\mu}_{j} t - \hat{\alpha}_{j} y_{t} - \hat{\beta}e_{j,t} - \hat{\gamma}y_{j,t} $$

(4)

where $\hat {\rho }_{j} = T^{-1}{\sum }_{t = 1}^{T}(b_{j,t}-\hat {\mu }_{j} t - \hat {\alpha }_{j} y_{t} - \hat {\beta }e_{j,t} - \hat {\gamma }y_{j,t} )$ and $\hat {\beta }$ and $\hat {\gamma }$ are CCEP estimators. We calculate the CADF statistics up to the 4th order.

As shown by the table, using the CIPS %10 critical value¹², we conclude in favor of the stationarity of $\hat {u}_{jt}$ for all countries up to lag 3, whereas the majority of these countries’ tests statistics indicate the presence of unit roots at the 3th- and 4th-order lag (Table 3).

Table 3 CIPS tests for $\hat {u}_{jt}$

We proceed by testing the presence of cointegration by using 2 different panel cointegration tests. The first test is due to Westerlund (2007) where cross-section dependence is taken into consideration through a bootstrap version of the test (see Persyn and Westerlund 2008). The second one is developed (Banerjee and Carrion-i Silvestre 2015) and has the property of controlling both cross section dependence and structural breaks. The results are illustrated in Table 4. While Banerjee-Silvestre test indicate the presence of cointegration for most of the countries except a few cases, Westerlund test confirm these results only for some countries, but still does so for more than the majority of them.

Table 4 Cointegration test results

4.2 Panel Error Correction Model

Having established the stationarity of the long-run residuals $\hat {u}_{jt}$, we estimate the panel error correction model in (4), setting p = q = s = 1.¹³ Unlike the estimation of the long-run equation, when we estimate the short-run dynamics, we use CCEMG instead of CCEP estimators. Hence, although we expect a homogenous response of the trade balance across countries with regard to the long run, the same should not be expected for short-run responses. Since CCEMG estimators do not assume this homogeneity, we prefer to employ them in the estimation of the short-term effects. Table 5 presents the estimation results of panel error correction Eq. (5) for each country. We find evidence in favor of a significant positive relationship between exchange rate depreciation and the trade balance for 7 out of 33 countries in the short run. These countries include the United States, Germany, Italy, Switzerland, Spain, Philippines, Thailand. For all countries, the error correction coefficient (ϕ) estimates have the correct sign and are significant. They vary in the range of -0.19 to -0.45, indicating the fact that, once disturbed, only 19-45 percent of the disequilibrium is corrected each quarter, which implies a relatively slow convergence to disequilibrium, with half-lives ranging from 3.5 to 1.5 quarters.¹⁴ On the other hand, except South Africa, because the short-run coefficients with negative signs do not appear to be significant in any of these countries, we could not find any support in favor of the J-curve hypothesis . As noted above, the J-curve hypothesis requires that deteriorating effects on the trade balance should appear in the short run only before achieving long-run improvements.¹⁵

Table 5 The short-run trade balance equation estimation results

5 Conclusion

In this study, we have re-examined the long-run Marshall-Lerner condition and the short-run J curve relationship by using bilateral trade flow data for a group of 33 countries. The approach reveals the fact that the real depreciation of the home currency has favorable effects on the home country’s trade balance in the long run; hence, the ML condition holds as a global phenomenon. However, this favorable effect can typically be observed in the long run. Only in 7 countries do we observe an immediate or lagged favorable impact in the short run on the trade balance. On the other hand, our analysis does not support the J-curve hypothesis, which states that a long-run favorable impact should be preceded by a deteriorating impact.

Following the recent orientations in the literature, extensions of the framework presented in this paper can be accomplished by incorporating industry/commodity level data into the analysis and considering a nonlinear functional form or a non-parametric method for the estimation of panel data models. While the former may provide valuable information in terms of the development industrial policy taken into consideration trade balance constraints, the latter can be useful in the analysis of possible asymmetric responses of trade balance to exchange rate changes.

Appendices

Appendix

A.1 Results with CCEMG estimators

In this appendix we provide the estimation results when CCEMG is also preferred in the long-run estimation.

Table 6 provides the long-run coefficient estimates. In 22 countries, the real depreciation of the domestic currency leads to an improvement in the trade balance in the long run, supporting the validity of Marshall-Lerner condition. For most of these countries, the results indicate an improvement in the trade balance of more than 1 percent as a result of 1 percent real depreciation.

Table 6 The long-run equation estimation results

Table 7 presents the estimation results of panel error correction equations. We find evidence in favor of a significant positive relationship between exchange rate depreciation and the trade balance for only 3 countries in the short run. On the other hand, we could not find any support in favor of the J-curve hypothesis other than South Africa where a negative exchange rate coefficient appears to be significant. For all countries, the error correction coefficient estimates have the correct sign and are significant.

Table 7 The short-run equation estimation results

A. 2 Long-run Causality

In this paper, following the related literature we have assumed that the causality runs from real exchange rate to trade balance not vice versa. In this appendix we question this assumption and to what extend the data supports the possibility of an reverse causality running from trade balance to real exchange rate as in Zhang and Macdonald (2014). To accomplish this task we also estimate the below panel error correction equation with real exchange rate being the dependent variable.

$$\begin{array}{@{}rcl@{}} {\Delta} e_{j,t} = \mu^{\prime}_{j}&+&\sum\limits_{l = 0}^{z}\kappa^{{\prime}l}_{j}{\Delta} y_{t-l} +\sum\limits_{l = 1}^{s}\varphi^{{\prime}b,l}_{j}{\Delta} b_{j,t-l}\\&+& \sum\limits_{l = 0}^{q}\varphi^{{\prime}e,l}_{j}{\Delta} e_{j,t-l}+ \sum\limits_{l = 0}^{p}\varphi^{{\prime}y,l}_{j}{\Delta} y_{j,t-l}+ \phi^{\prime}_{j} \hat{u}_{j,t-1}+ \xi^{\prime}_{j,t}, \end{array} $$

Together with Eq. (5), the above equation defines a panel vector error correction model with exogenous variables (PVECMX). Since all the ϕ_j in the trade balance equation (Table 5) are already found to be significant, testing the significance of the error correction coefficients $\phi ^{\prime }_{j}$ in the real exchange rate equation provides a test for the long-run non-causality from trade balance to real exchange rate versus bi-directional causality. Table 8 provides the estimation results of the above equation. As can be followed from the table, in only 8 of the 33 countries error correction coefficients appear to be significant.¹⁶ This evidence supports the long-run non-causality from trade balance to real exchange rate.

Table 8 The short-run equation estimation results

Additionally we calculate the cointegration tests for the “reverse” equation of real exchange rate. Table 9 presents the results. As can be seen from the table, the results are in favor of cointegration only for a few countries and only for some test statistics. This result constitutes a sharp contrast with those that are presented in Table 5, where, cointegration is supported by the data for almost all countries. This provides a further evidence on the uni-directional long-run causality running from real exchange rate to trade balance.

Table 9 Cointegration test results (Dependent variable: e)

A. 3. Results with semi-logarithmic model

In this appendix we provide all the estimation results with trade the trade balance is defined as the difference between exports and imports, without taking its logarithm where all the other variables are expressed in logarithms.

Table 10 provides the long-run coefficient estimates. In 18 countries the real exchange rate appear to have significant long run effects on the trade balance. In 14 of them, the real depreciation of the domestic currency leads to an improvement in the trade balance in the long run, supporting the validity of Marshall-Lerner condition. The coefficients estimates indicate the response of trade balance in billion US dollars as a response to 1 percent change in the real exchage rate. The magnitudes vary across countries from 150 billion to 3.5 trillion (Japan).

Table 10 The long-run equation estimation results

Table 11 illustrates the CIPS panel unit root test statistics for the estimated residuals $\hat {u}_{jt}$. We conclude in favor of the stationarity for the majority of the countries up to lag 2, whereas the majority of these countries’ tests statistics indicate the presence of unit roots at higher orders.

Table 11 CIPS tests for $\hat {u}_{jt}$

Table 12 shows the result of panel cointegration tests. Overall the results indicate the presence of cointegration for the majority of the countries.

Table 12 Cointegration tests results

Table 13 presents the estimation results of panel error correction equations. We find evidence in favor of a significant positive relationship between exchange rate depreciation and the trade balance for 10 countries in the short run. On the other hand, we could not find any support in favor of the J-curve hypothesis other than Malaysia, Switzerland and the UK, where a negative exchange rate coefficients appear to be significant. For all countries, the error correction coefficient estimates have the correct sign and are significant.

Table 13 The short-run equation estimation results

Table 14 The short-run equation estimation results